A Short Note on Addition of Vectors

The term “vector addition” refers to the joining of two or more vectors. When we add vectors, we are combining two or more vectors together using the addition operation in order to get a new vector that is equal to the sum of the previous vectors. Vector addition has applications in the physical sciences, where vectors are used to express physical quantities such as velocity, displacement, and acceleration.

This article will teach you about vector addition, their properties, and numerous rules, all while providing you with solved examples.

Addition of Vectors

An alphabet with an arrow over it (or) an alphabet written in bold are both ways of representing vectors, which are a mix of direction and magnitude. It is possible to add two vectors together, denoted by the symbol “a+b,” by using vector addition, and the final vector can be expressed as: a + b. Before we can learn about the properties of vector addition, we must first understand the requirements that must be met when vectors are added together. The following are the terms and conditions:

• Vectors can only be combined if they are of the same type as each other. For example, acceleration should be added with only acceleration and not with mass as well.
• It is not possible to combine vectors with scalars.

Consider the following two vectors: C and D. Where C = C_xi + C_yj + C_zk and D = D_xi + D_yj + D_zk are the values of the variables. Then, the resultant vector (or vector sum) R = C + D = (C_x + D_x)i + (C_y + D_y)j + (C_z + D_z) k 

Formulas for Vector Addition

To combine two vectors a = <a₁, a₂, a₃> and b = <b₁, b₂, b₃>.

• In component form, the vectors a and b are equal to the total of their component parts, which are as follows:<a₁+b₁, a₂+b₂, a₃ + b₃>.
• If the two vectors are ordered by attaching the head of one vector to the tail of the other, then the vector that unites the free heads and tails is the vector that sums the two vectors (by triangle law).
• If the two vectors represent the two neighbouring sides of a parallelogram, then the sum indicates the diagonal vector that is drawn from the place where the two vectors meet, which is the intersection point of both vectors (by parallelogram law).

Important Points to Keep in Mind About Vector Addition

There are several points that should be kept in mind when studying the addition of vectors, which are as follows:

• Vectors are represented as a combination of direction and magnitude, and they are represented graphically by an arrow.

As long as we have the components of a vector, we can figure out what the final vector will look like.

• The addition of vectors can be accomplished through the use of the well-known triangle law, which is referred to as the head-to-tail approach.

Conclusion

An alphabet with an arrow over it (or) an alphabet written in bold are both ways of representing vectors, which are a mix of direction and magnitude. It is possible to add two vectors together, denoted by the symbol “a+b,” by using vector addition, and the final vector can be expressed as: a + b. Vectors can only be combined if they are of the same type as each other. For example, acceleration should be added with only acceleration and not with mass as well.It is not possible to combine vectors with scalars. If the two vectors are ordered by attaching the head of one vector to the tail of the other, then the vector that unites the free heads and tails is the vector that sums the two vectors (by triangle law). If the two vectors represent the two neighbouring sides of a parallelogram, then the sum indicates the diagonal vector that is drawn from the place where the two vectors meet, which is the intersection point of both vectors (by parallelogram law).